In this research work, a multi-index-based support vector machine (SVM) classification approach has been proposed to determine the complex and morphologically heterogeneous land cover/use (LCU) patterns of cities, with a special focus on separating bare lands and built-up regions, using Istanbul, Turkey as the main study region, and Ankara and Konya (in Turkey) as the independent test regions. The multi-index approach was constructed using three-band combinations of spectral indices, where each index represents one of the three major land cover categories, green areas, water bodies, and built-up regions. Additionally, a shortwave infrared-based index, the Normalized Difference Tillage Index (NDTI), was proposed as an alternative to existing built-up indices. All possible index combinations and the original ten-band Sentinel-2A image were classified with the SVM algorithm, to map seven LCU classes, and an accuracy assessment was performed to determine the multi-index combination that provided the highest performance. The SVM classification results revealed that the multi-index combination of the normalized difference tillage index (NDTI), the red-edge-based normalized vegetation index (NDVIre), and the modified normalized difference water index (MNDWI) improved the mapping accuracy of the heterogeneous urban areas and provided an effective separation of bare land from built-up areas. This combination showed an outstanding overall performance with a 93% accuracy and a 0.91 kappa value for all LCU classes. The results of the test regions provided similar findings and the same index combination clearly outperformed the other approaches, with 92% accuracy and a 0.90 kappa value for Ankara, and an 84% accuracy and a 0.79 kappa value for Konya. The multi-index combination of the normalized difference built-up index (NDBI), the NDVIre, and the MNDWI, ranked second in the assessment, with similar accuracies to that of the ten-band image classification.